Base field 3.3.564.1
Generator \(w\), with minimal polynomial \(x^{3} - x^{2} - 5x + 3\); narrow class number \(1\) and class number \(1\).
Form
Weight: | $[2, 2, 2]$ |
Level: | $[17, 17, -w^{2} + 2]$ |
Dimension: | $8$ |
CM: | no |
Base change: | no |
Newspace dimension: | $13$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
\(x^{8} + x^{7} - 12x^{6} - 10x^{5} + 45x^{4} + 24x^{3} - 61x^{2} - 11x + 15\) |
Show full eigenvalues Hide large eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
2 | $[2, 2, w - 1]$ | $\phantom{-}e$ |
3 | $[3, 3, w]$ | $-\frac{1}{4}e^{7} - e^{6} + 2e^{5} + \frac{19}{2}e^{4} - \frac{11}{4}e^{3} - \frac{81}{4}e^{2} + \frac{3}{2}e + \frac{25}{4}$ |
3 | $[3, 3, w - 2]$ | $\phantom{-}\frac{1}{2}e^{7} + e^{6} - 4e^{5} - 9e^{4} + \frac{9}{2}e^{3} + \frac{33}{2}e^{2} + 4e - \frac{7}{2}$ |
13 | $[13, 13, w^{2} - 2w - 2]$ | $-\frac{1}{4}e^{7} + e^{6} + 3e^{5} - \frac{19}{2}e^{4} - \frac{43}{4}e^{3} + \frac{87}{4}e^{2} + \frac{17}{2}e - \frac{19}{4}$ |
17 | $[17, 17, -w^{2} + 2]$ | $\phantom{-}1$ |
19 | $[19, 19, -w^{2} + w + 1]$ | $-e^{7} - 2e^{6} + 9e^{5} + 18e^{4} - 16e^{3} - 35e^{2} - e + 14$ |
31 | $[31, 31, -w + 4]$ | $\phantom{-}\frac{1}{2}e^{7} - 6e^{5} + \frac{41}{2}e^{3} + \frac{1}{2}e^{2} - 18e + \frac{1}{2}$ |
41 | $[41, 41, -w^{2} + 2w - 2]$ | $\phantom{-}\frac{3}{2}e^{7} - 15e^{5} + \frac{75}{2}e^{3} - \frac{3}{2}e^{2} - 15e - \frac{15}{2}$ |
41 | $[41, 41, -2w^{2} - 3w + 4]$ | $-e^{7} - 2e^{6} + 8e^{5} + 17e^{4} - 9e^{3} - 26e^{2} - 8e + 3$ |
41 | $[41, 41, 2w + 1]$ | $-\frac{1}{2}e^{7} + 2e^{6} + 6e^{5} - 19e^{4} - \frac{41}{2}e^{3} + \frac{87}{2}e^{2} + 14e - \frac{27}{2}$ |
43 | $[43, 43, -w^{2} - w + 5]$ | $\phantom{-}e^{5} - 9e^{3} - e^{2} + 16e + 5$ |
47 | $[47, 47, -w^{2} + 8]$ | $-\frac{5}{4}e^{7} + 12e^{5} - \frac{3}{2}e^{4} - \frac{111}{4}e^{3} + \frac{51}{4}e^{2} + \frac{23}{2}e - \frac{27}{4}$ |
47 | $[47, 47, 2w^{2} - w - 8]$ | $\phantom{-}\frac{1}{2}e^{7} + e^{6} - 4e^{5} - 10e^{4} + \frac{9}{2}e^{3} + \frac{47}{2}e^{2} + 4e - \frac{27}{2}$ |
53 | $[53, 53, w^{2} + w - 7]$ | $-\frac{1}{4}e^{7} - 2e^{6} + 2e^{5} + \frac{35}{2}e^{4} - \frac{7}{4}e^{3} - \frac{129}{4}e^{2} + \frac{1}{2}e + \frac{21}{4}$ |
59 | $[59, 59, w^{2} - 2w - 4]$ | $-\frac{3}{4}e^{7} - 3e^{6} + 5e^{5} + \frac{55}{2}e^{4} + \frac{3}{4}e^{3} - \frac{211}{4}e^{2} - \frac{19}{2}e + \frac{39}{4}$ |
61 | $[61, 61, -3w^{2} + 14]$ | $\phantom{-}2e^{7} + 3e^{6} - 18e^{5} - 27e^{4} + 36e^{3} + 50e^{2} - 16e - 16$ |
61 | $[61, 61, 4w^{2} - 2w - 19]$ | $\phantom{-}\frac{1}{2}e^{7} - 2e^{6} - 6e^{5} + 19e^{4} + \frac{41}{2}e^{3} - \frac{89}{2}e^{2} - 13e + \frac{31}{2}$ |
61 | $[61, 61, -2w^{2} + 7]$ | $-\frac{3}{2}e^{7} - e^{6} + 14e^{5} + 8e^{4} - \frac{59}{2}e^{3} - \frac{13}{2}e^{2} + 5e - \frac{5}{2}$ |
67 | $[67, 67, -2w^{2} - w + 8]$ | $\phantom{-}\frac{5}{4}e^{7} - 12e^{5} + \frac{3}{2}e^{4} + \frac{115}{4}e^{3} - \frac{55}{4}e^{2} - \frac{33}{2}e + \frac{47}{4}$ |
71 | $[71, 71, w^{2} + 2w - 4]$ | $-4e^{7} - 6e^{6} + 37e^{5} + 54e^{4} - 78e^{3} - 99e^{2} + 34e + 24$ |
Atkin-Lehner eigenvalues
Norm | Prime | Eigenvalue |
---|---|---|
$17$ | $[17, 17, -w^{2} + 2]$ | $-1$ |